Nuclear materials were formed in supernovas. They wouldn’t exist in the first place without a star.
Well, yeah, sure. But that star is not the Sun.
Earth wouldn’t have coalesced without the sun in the middle. Otherwise we’d still be a gas blob.
I mean, sure? It wouldn’t be a gas blob, but it would be a very different system. But that still has nothing to do with it – even if the gravity of the sun influences how the earth coalesces, it’s still not where the thermal energy of the core came from. That came from the potential of the dust itself.